Question: Simplify the following expression: $a = \dfrac{1}{3n} - \dfrac{8}{5n}$
Solution: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $3n$ and $5n$ $\lcm(3n, 5n) = 15n$ $ a = \dfrac{5}{5} \cdot \dfrac{1}{3n} - \dfrac{3}{3} \cdot \dfrac{8}{5n} $ $a = \dfrac{5}{15n} - \dfrac{24}{15n}$ $a = \dfrac{5 -24}{15n}$ $a = \dfrac{-19}{15n}$